Generalized Frobenius Numbers: Bounds and Average Behavior

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Mathematics (CMC)

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The proof of Theorem 1.1 is based on a generalization of a result of Kannan which relates the classical Frobenius number to the covering radius of a certain simplex with respect to a certain lattice. In our setting we need a kind of generalized covering radius, whose definition as well as some properties and background information from the Geometry of Numbers will be given in Section 2. In Section 3 we will prove, analogously to the mentioned result of Kannan, an identity between Fs(a) and this generalized covering radius and will present a proof of Theorem 1.1. The last section contains a proof of Corollary 1.2.

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© 2012 IMPAN